Chemistry 132, Winter 2008
Solutions to Homework No. 4
Problem 1.
(1.1) True.
v
is the magnitude of a velocity vector (Levine
eq. 15.1). The magnitude of a vector is always positive or
zero.
(1.2) False. The components of the velocity vector can be
positive, negative, or zero (Levine p. 457).
(1.3) True. The
y
component of the velocity of a molecule
is a real number. The square of any real number is always
greater than or equal to zero.
(1.4) False. In the kinetic theory of gases, the components of
the velocity vector are assumed to be independent of each
other (Levine p. 463).
(1.5) False. For a monoatomic gas, such as helium or neon,
the molar heat capacity at constant pressure is
C
P,
m
= 5
R/
3
(Levine eq. 15.19), assuming ideal gas behavior. Therefore,
C
P,
m
is independent of the molar mass of the gas.
(1.6) True. If
T
is not too high, then
C
P,
m
= 5
R/
3 for a
monoatomic gas such as helium (Levine p. 461).
(1.7) False. Since
h
±
tr
i
=
3
2
kT
(Levine eq. 15.15), at a given
temperature the average molecular translational energy is
independent of the mass of the gas molecules.
(1.8) False. The average molecular translational energy de-
pends only on temperature.
(1.9) True. Follows from
h
±
tr
i
=
3
2
kT
(Levine eq. 15.15), as
for part (1.7) and part (1.8).
(1.10) True. Since
h
±
tr
i
=
1
2
m
h
v
2
i
(Levine eq. 15.12) and
since
h
±
tr
i
=
3
2
kT
(Levine eq. 15.15), then
h
v
2
i
depends only
on
T
and not on the type of gas.
(1.11) False.
According to the Maxwell distribution law
(Levine eq. 14.44) rewritten in terms of the translational ki-
netic energy (Levine eq. 15.52), a molecule can be found to
have any kinetic energy at any temperature. The only thing
that changes from one temperature to another is the frac-
tion
dN
±
tr
/N
of molecules whose kinetic energy falls within
a given small interval (
±
tr
,±
tr
+
d±
tr
).
(1.12) True. Since
h
±
tr
i
=
3
2
kT
(Levine eq. 15.15) does not
depend on the type of gas, the ratio
h
±
tr
i
300 K
h
±
tr
i
100 K
=
(300 K)
(100 K)
.
is the same for both gases.
(1.13) False. The most probable speed is
v
mp
=
p
2
RT/M
(Levine p. 472), which depends on the molar mass of the gas
and on temperature. Therefore, at a given temperature,
v
mp
for He(g) diﬀers from
v
mp
for Ne(g).
(1.14) False. The most probable speed is
v
mp
=
p
2
RT/M
(Levine p. 472), which depends on the molar mass of the gas
and on temperature, so the explanation given for part (1.13)
applies also in this case.
(1.15) True. The distribution function for
v
x
,
g
(
v
x
), has a
maximum at
v
x
= 0 (Levine p. 469) independently of the
type of gas. Since all velocity components have the same
distribution function (Levine p. 463), the most probable
value of
v
z
is also zero. Since this most probable value is
always zero, it is the same for all gases.
(1.16) False. Probabilities are dimensionless but probability